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Journal of Shangluo University

The Effects of Generalized Nonlinear N-th Power Sum Squeezing on Seventh Kind of Multimode Superposition State Light Field with Superpositions of Macroscopically Distinct Two Quantum States

Jiliang Zhang

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

In this paper,the multimode squeezed state theory established by yang Zhiyong and Hou Xun and published in Acta Photonica Sinica is utilized to study the effects of Generalized nonlinear N-th power sum squeezing is seventh kind of Multimode superposition state light field which is composed of the linear superpositions of multimode coherent state and contrary state of multimode imaginary coherent state . It is found that under the conditions of the products q ·N=2p and p=2m+l(m=0,1,2,3, …)where q represents the cavity-mode number and N represents the squeezing power number,while some certain quantization conditions are satisfied by the initial phase sum of each mode,and while the mixing phase sum + made of the initial phase difference( ) between the two components of the state and the mean photon number of each multimode coherent state light field mentioned above changes continuously in the foxed and closed region,the state can always present the effects of generalized nonlinear N-th power sum squeezing that chandes periodically.This shows that the state is a typical multimode nonchasical light field.

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Jiguang zazhi•Jan 1, 2004•0 citations
In this paper,the multimode squeezed state theory established by yang Zhiyong and Hou Xun and published in Acta Photonica Sinica is utilized to study the effects of Generalized nonlinear N-th power sum squeezing is seventh kind of Multimode superposition state light field which is composed of the linear superpositions of multimode coherent state and contrary state of multimode imaginary coherent state . It is found that under the conditions of the products q ·N=2p and p=2m+l(m=0,1,2,3, …)where q represents the cavity-mode number and N represents the squeezing power number,while some certain quantization conditions are satisfied by the initial phase sum of each mode,and while the mixing phase sum + made of the initial phase difference( ) between the two components of the state and the mean photon number of each multimode coherent state light field mentioned above changes continuously in the foxed and closed region,the state can always present the effects of generalized nonlinear N-th power sum squeezing that chandes periodically.This shows that the state is a typical multimode nonchasical light field.
According to the linear superposition principle of state in quantum mechanics,the three state superposi-tion multimode Schr dinger-Cat State light-field,namely,multimode SCS light-field) │ Ψ ,3) q is constructed,which is composed of multimode complex conjugation imaginary coherent state,the contrary state of multimode complex conjugation imaginary coherent state,and multimode complex conjugation coherent state.The multimode squeezed state theory established recently by pro fessor Yang Zhiyong and academician Hou Xun is utilized to study the char-acteristics of generalized nonlinear unequal-power higher-power sum squeezing of the generalized electric-field com-ponent in the multimode SCS light-field │ Ψ ,3) q mentioned above in detail.The results show that under the condi-tion of the sum of squeezing-power-number for every mode being an even number,while some other fixed conditions are respectively satisfied by the sum of the products between the squeezing-power-number of each mode and the ini-tial phase which is in accordance with each mode above,by the interstate initial phase difference,and by the mean photon-number of each multimode coherent state light-field,the generalized electric-field component of the multi-mode SCS light-field │ Ψ ,3) q can always display the effects of any N j -th power generalized nonlinear unequal-power higher-power sum squeezing that change periodically and alternatively.
According to the Linear superpositon principle in quantum mechanics ,the ninth kind of two ligtht Field is constructed that is composed of multimode vaccum state light field And then the multimode squeezed state theory suggested by Yang Zhiyong and Hou Xun and Published in Acta Photonica Sinica is utlized to study the properties of generalized nonlinear equal- power N-th power Y-squeeting of the state mentioned above. It is found that ①、whether the squeezing-power-number N is an odd-number or an even-number, while some certain quantization conditions are satisfied by the initial phase of each mode and by the initial phase difference( ) between two components of the state respectively ,the state can always present any odd-number power any even-number N-th power Y-squeezing effects which changes periodically. ② Compared with the reference [11] ,the state constructed in this paper is rathier different from the state constructed in reference [11] ,under some fixed conditions the states and can display the phenomena of N-th power Y-similitude- squeezing and N-th power Y-degenerate-squeezing.
In this paper, the multimode squeezed state theory is utilized to study the characteristics of generalized nonlinear-unequal-power higher-power sum-squeezing of generalized magnetic-field component in the state |ψ(f)(2)q made up of the linear superposition of multimode functional coherent state |{fj(x,y,z)}q and its contrary state |{-fj(x,y,z)}q according to the superposition principle of quantum state in quantum mechanics. It is found that: 1) under the condition of the sum of squeezing-power-number being an any even-number, thestate |ψ(f)(2)q can always stay in the generalized nonlinear unequal-power Nj-H minimum uncertainty state;and 2) under the condition of the sum of squeezing-power-number being an anyodd-number, while some other fixed conditions are satisfied by the state |ψ(f)(2)q the state mentioned can display the effects of generalized nonlinear unequal-power Nj-th power H-squeezing that changes periodically and alternatively.
The first kind of the three state superposition multimode superposition state light field ψ(3)1q is constructed that is composed of multimode coherent state light field {Zj}q, multimode vacuum state light field {0j}q and contrary state {-Zj}q of multimode coherent state light field {Zj}q and that is based on the linear superposition principle of quantum state in quantum mechanics. Then the multimode squeezed state theory is utilized to study the effects of equalpower higherpower sum squeezing of generalized electric field component in the state ψ(3)1q . It is found that under certain and fixed conditions, the generalized electric field component (or the second perpendicular phase component) of the state ψ(3)1q can always display generalized nonlinear equalpower oddnumbermode with evennumberpower, evennumbermode with oddnumberpower, evennumbermode with evennumberpower, or oddnumbermode with oddnumberpower higherpower sum squeezing effects respectively and periodically.
On the bases of the linear superposition principle of quantum state in quantum mechanics, |ψ (3) 3q -the third kind of the three state superposition multimode superposition state light field is constructed that is composed of linear superposition of multimode complex conjugation coherent state |{Z * j} q ?multimode complex conjugation imaginary coherent state |{iZ * j} q and multimode vaccum state |{0 j} q . By utilizing the theory of multimode squeezed states, the properties of generalized nonlinear unequal-power N j-th power H-squeezing in the state |ψ (3) 3q is studied in detail. It is found that when the sum of the squeezing power of each mode is even number only and certain conditions are satisfied, the first perpendicular phase component and the second one of the state |ψ (3) 3q can always display any power generalized nonlinear unequal-power N j-th power H-squeezing effects that change periodically, respectively.
In this paper,the multimode squeezed state theory is utilized to study the characteristics of generalized nonlinear-unequal-power N j -th power H-squeezing of generalized electric-field component in the state |Ψ (2) (f) g, made up of the linear superposition of multimode functional coherent state |{f j (x,y,z) } g and its contrary state |{-f j( x,y,z )} g according to the superposition principle of quantum state in quantum mechanics.It shows the results:under the condition of the sum of squeezing-power-number being an any odd-number,while some other fixed conditions are satisfied by the suate |Ψ (2) (f) g the state |Ψ (2) (f) g can display the effects of any generalized nonlinear unequal-power N j -th power H-squeezing that changes periodically and alternatively.